Mathematical Biology

Population dynamics, epidemic models, and pattern formation.

foundation tier

Mathematical Biology. Population dynamics, epidemic models, and pattern formation. This page collects canonical references that organise the subject and provide entry points to its main techniques.

Foundations and canonical references

The standard treatments of mathematical biology approach the subject from complementary angles. Murray, Mathematical Biology I: An Introduction (2002) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications (2003) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for mathematical biology include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2002
    Mathematical Biology I: An Introduction
    murray-2002
  • textbook · primary · 2003
    Mathematical Biology II: Spatial Models and Biomedical Applications
    murray-2003

In context

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Explore

  1. 01

    Population Dynamics

    Lotka–Volterra, structured populations, and age-structured models.
  2. 02

    Mathematical Epidemiology

    SIR/SEIR, network epidemics, and reproductive numbers.
  3. 03

    Pattern Formation in Biology

    Turing patterns and reaction-diffusion morphogenesis.
  4. 04

    Phylogenetic Mathematics

    Tree spaces, coalescent theory, and likelihood for phylogenies.

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